Beamformer quantization error analysis and dynamic range considerations

Abstract

A methodology is presented which can be used to analyze the effects of inaccuracies caused by finite precision arithmetic and finite precision data representation on beamformer performance. The random errors associated with quantization are of primary concern. For the baseband beamformer with interpolation analyzed, quantization errors occur in the A/D conversion process, the basebanding and interpolation functions, and in the shade, delay, and sum beamforming operations. These errors contribute to a noise floor which interferes with the detection of low‐level signals. Hence, quantization errors can have an impact on the dynamic range, i.e., the ratio of the peak signal level to minimum detectable signal level. A brief description of the noise model commonly used to characterize the quantization errors is presented. The sources of error are identified for the digital baseband beamformer with interpolation, and expressions are presented for the variances of the individual sources. A procedure is presented for determining the total effect of the combination of the individual sources of error on the beamforming process.